G geo09 New member Joined May 30, 2009 Messages 1 May 30, 2009 #1 two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger?
two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger?
W wjm11 Senior Member Joined Nov 13, 2004 Messages 1,417 May 30, 2009 #2 Re: geometry Two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger? Click to expand... The ratio of the volumes of similar figures is the cube of the ratio of the linear dimensions. Therefore, the linear dimension ratio is (Lsmall/Lbig) = (Vsmall/Vbig)^(1/3) = (27/125)^(1/3) = 3/5. The ratio of the areas of similar figures is the square of the ratio of the linear dimensions. Therefore, the area dimension ratio is (Lsmall/Lbig)^2 = (Asmall/Abig) = (3/5)^2 = 9/25. Hope that helps.
Re: geometry Two similar pyramids have volumes 27 and 125. if the smaller has lateral area 18, what is the lateral area of larger? Click to expand... The ratio of the volumes of similar figures is the cube of the ratio of the linear dimensions. Therefore, the linear dimension ratio is (Lsmall/Lbig) = (Vsmall/Vbig)^(1/3) = (27/125)^(1/3) = 3/5. The ratio of the areas of similar figures is the square of the ratio of the linear dimensions. Therefore, the area dimension ratio is (Lsmall/Lbig)^2 = (Asmall/Abig) = (3/5)^2 = 9/25. Hope that helps.
